As on arXiv
Abstract
We find new examples of steady gradient Ricci solitons with positive curvature operator in dimensions four and above. Utilising a procedure first introduced by Lai, we construct examples with symmetry in dimension for any pair of integers and discuss their asymptotic geometry.
Comments: Minor modifications, accepted into Journal of Geometric Analysis
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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Rigidity of positively curved Steady gradient Ricci solitons on orbifolds
Topics Sphere theorems, Ricci solitons · Shared terms “steady gradient”, “gradient Ricci”, “positive curvature”
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Topics Ricci solitons · Shared terms “steady gradient”, “gradient Ricci”, “positive curvature”
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Topics Sphere theorems, Ricci solitons · Same author Luke T. Peachey · Shared terms “gradient Ricci”
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Topics Sphere theorems, Ricci solitons · Shared terms “positive curvature”, “curvature operator”
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Topics Sphere theorems, Ricci solitons · Shared terms “steady gradient”, “positive curvature”, “curvature operator”
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Topics Sphere theorems, Ricci solitons
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Topics Sphere theorems · Shared terms “positive curvature”
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Topics Sphere theorems, Ricci solitons
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Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11A.11Hamilton’s 1982 Theorem
Positive Ricci curvature in dimension 3 flows to a round metric.
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.